"Teichmuller theory"의 두 판 사이의 차이
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==introduction== | ==introduction== | ||
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==review of hyperbolic geometry== | ==review of hyperbolic geometry== | ||
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* A horocycle at marked point p is a set of points "equidistant" to p. In lift to H^2, looks like circle tangent to boundary at p. | * A horocycle at marked point p is a set of points "equidistant" to p. In lift to H^2, looks like circle tangent to boundary at p. | ||
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==Teichmuller space of a marked surface== | ==Teichmuller space of a marked surface== | ||
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Given marked surface (S,M) , the Teichmuller space T(S,M) is the space of metrics on (S,M) such that | Given marked surface (S,M) , the Teichmuller space T(S,M) is the space of metrics on (S,M) such that | ||
| − | * are | + | * are hyperbolic (constant curvature -1) |
* have geodesic boundary at boundary of S | * have geodesic boundary at boundary of S | ||
* local neighborhood of point on boundary S can be mapped isometrically to neighborhood of a point here on one side of geodesic | * local neighborhood of point on boundary S can be mapped isometrically to neighborhood of a point here on one side of geodesic | ||
| − | * | + | * have cusps at points in M |
Considered up to diffeomorphism homotopic to identity. | Considered up to diffeomorphism homotopic to identity. | ||
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(2) T(S,M) is manifold of dimension 6g-6+2p+3b+c where g = genus, p=# of puncture, b = # boundary component, c=# of marked points on boundary | (2) T(S,M) is manifold of dimension 6g-6+2p+3b+c where g = genus, p=# of puncture, b = # boundary component, c=# of marked points on boundary | ||
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==related items== | ==related items== | ||
* [[Moduli space of local systems and higher Teichmuller theory]] | * [[Moduli space of local systems and higher Teichmuller theory]] | ||
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==expositions== | ==expositions== | ||
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[[분류:migrate]] | [[분류:migrate]] | ||
| − | == 메타데이터 == | + | ==메타데이터== |
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===위키데이터=== | ===위키데이터=== | ||
* ID : [https://www.wikidata.org/wiki/Q2400539 Q2400539] | * ID : [https://www.wikidata.org/wiki/Q2400539 Q2400539] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'teichmüller'}, {'LEMMA': 'space'}] | ||
2021년 2월 17일 (수) 02:32 기준 최신판
introduction
review of hyperbolic geometry
- horocycle
- exponentiated hyperbolic distances between horocycles drawn around vertices of a polygon with geodesic sides and cusps at the vertices
- lamination
- shear coordinates
- lambda length
- http://moniker.name/worldmaking/?p=744
- http://orion.math.iastate.edu/dept/thesisarchive/MSCC/OLearyMSCCSS06.pdf
- \def
- An ideal triangle in (S,M) is a triangle with vertices at M, whose sides are geodesics.
- \def
- A horocycle at marked point p is a set of points "equidistant" to p. In lift to H^2, looks like circle tangent to boundary at p.
Teichmuller space of a marked surface
Given marked surface (S,M) , the Teichmuller space T(S,M) is the space of metrics on (S,M) such that
- are hyperbolic (constant curvature -1)
- have geodesic boundary at boundary of S
- local neighborhood of point on boundary S can be mapped isometrically to neighborhood of a point here on one side of geodesic
- have cusps at points in M
Considered up to diffeomorphism homotopic to identity.
Facts
(1) T(S,M) contractible
(2) T(S,M) is manifold of dimension 6g-6+2p+3b+c where g = genus, p=# of puncture, b = # boundary component, c=# of marked points on boundary
expositions
- Norbert A'Campo, Lizhen Ji, Athanase Papadopoulos, On Grothendieck's construction of Teichmüller space, http://arxiv.org/abs/1603.02229v1
- Matheus, Carlos. “Lecture Notes on the Dynamics of the Weil-Petersson Flow.” arXiv:1601.00690 [math], January 4, 2016. http://arxiv.org/abs/1601.00690.
- Papadopoulos, Athanase, Vincent Alberge, and Weixu Su. “A Commentary on Teichm"uller’s Paper ‘Extremale Quasikonforme Abbildungen Und Quadratische Differentiale.’” arXiv:1511.01313 [math], November 4, 2015. http://arxiv.org/abs/1511.01313.
- Introduction to Teichmüller theory, old and new, Athanase Papadopoulos
articles
- Leonid Chekhov, Marta Mazzocco, Colliding holes in Riemann surfaces and quantum cluster algebras, arXiv:1509.07044 [math-ph], September 23 2015, http://arxiv.org/abs/1509.07044
- Lien-Yung Kao, Pressure type metrics on spaces of metric graphs, arXiv:1604.03173 [math.DS], April 11 2016, http://arxiv.org/abs/1604.03173
- Babak Modami, Asymptotics of a class of Weil-Petersson geodesics and divergence of Weil-Petersson geodesics, Algebr. Geom. Topol. 16 (2016) no.1, pp. 267-323, http://arxiv.org/abs/1401.3234v4
- Antonakoudis, Stergios M. “The Complex Geometry of Teichm"uller Spaces and Bounded Symmetric Domains.” arXiv:1510.07340 [math], October 25, 2015. http://arxiv.org/abs/1510.07340.
- Penner, R. C., and Anton M. Zeitlin. “Decorated Super-Teichm"uller Space.” arXiv:1509.06302 [hep-Th, Physics:math-Ph], September 21, 2015. http://arxiv.org/abs/1509.06302.
메타데이터
위키데이터
- ID : Q2400539
Spacy 패턴 목록
- [{'LOWER': 'teichmüller'}, {'LEMMA': 'space'}]